How do I start level 70 Summoner quest?

[Shriex]

Your MSQ guide (the red and beige meteor banner) is a clickable link to the location of the current/next MSQ.
Whenever a new job quest becomes available, it will appear as a clickable link just below that, except for the Lv80 quest.

The job quests for an expansion require the completion of the previous expansion.

Thanks, I'm aware of all that - that wasn't / isn't the issue I was running into. It had to do with the gatekeeping with job quests.